1. The problem asks to graph the solution set of the inequality $x \leq -5$. 2. The inequality $x \leq -5$ means all values of $x$ that are less than or equal to $-5$. 3. On the coordinate plane, this corresponds to a vertical line at $x = -5$. 4. The shading is to the left of this line, including the line itself because of the "less than or equal to" sign. 5. This means every point with $x$-coordinate less than or equal to $-5$ satisfies the inequality. 6. To graph, draw a solid vertical line at $x = -5$ and shade the entire region to the left of this line. Final answer: The solution set is the region to the left of and including the vertical line $x = -5$.